CBSE Class 9 Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in CBSE Class 9, not a summary of it.

1. 1

   Number Systems

   2 topics

   • Real Numbers
   • Rationalization
2. 2

   Algebra

   2 topics

   • Polynomials
   • Linear Equations in Two Variables
3. 3

   Coordinate Geometry

   2 topics

   • Cartesian System
   • Plotting a Point in the Plane
4. 4

   Geometry

   2 topics

   • Lines and Angles
   • Triangles
5. 5

   Mensuration

   2 topics

   • Areas
   • Surface Areas and Volumes
6. 6

   Statistics & Probability

   2 topics

   • Statistics
   • Probability

Mathematics flashcards for CBSE Class 9

21 of 51 cards from the Mathematics deck — real questions with worked answers.

1. What is a rational number?

   A number that can be written in the form p/q where p and q are integers and q is not equal to 0.

2. What is an irrational number?

   A number that cannot be written in the form p/q (with integers p, q and q not 0). Its decimal expansion is non-terminating and non-recurring (e.g., square root of 2, pi).

3. How can you tell from its decimal expansion whether a number is rational?

   A rational number has a decimal expansion that is either terminating or non-terminating but recurring (repeating).

4. A terminating decimal p/q (in lowest terms) terminates only when q has what prime factors?

   Only the prime factors 2 and/or 5 (i.e., q is of the form 2^m x 5^n).

5. How many rational numbers lie between any two given rational numbers?

   Infinitely many.

6. What is the result of adding or multiplying a non-zero rational number with an irrational number?

   The result is always irrational.

7. State the law of exponents for a^m x a^n.

   a^m x a^n = a^(m+n).

8. State the law of exponents for (a^m)^n.

   (a^m)^n = a^(mn).

9. What is a^m divided by a^n equal to?

   a^(m-n).

10. How do you rationalise the denominator of 1/(a + sqrt(b))?

    Multiply numerator and denominator by the conjugate (a - sqrt(b)), giving (a - sqrt(b))/(a^2 - b).

11. What is the rationalising factor of sqrt(a)?

    sqrt(a) itself, since sqrt(a) x sqrt(a) = a.

12. What is the value of a^0 for any non-zero a?

    1.

13. What is a polynomial in one variable?

    An algebraic expression of the form a_n x^n + ... + a_1 x + a_0, where the powers of the variable are whole numbers and the coefficients are real numbers.

14. What is the degree of a polynomial?

    The highest power of the variable that appears in the polynomial.

15. Name a polynomial by degree: degree 1, degree 2, and degree 3.

    Degree 1 = linear, degree 2 = quadratic, degree 3 = cubic.

16. What is the degree of a non-zero constant polynomial?

    Zero.

17. State the Remainder Theorem.

    If a polynomial p(x) is divided by (x - a), the remainder is p(a).

18. State the Factor Theorem.

    (x - a) is a factor of polynomial p(x) if and only if p(a) = 0.

19. What is a zero (or root) of a polynomial p(x)?

    A value of x for which p(x) = 0.

20. Expand (a + b)^2 and (a - b)^2.

    (a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.

21. Give the identity for a^3 + b^3.

    a^3 + b^3 = (a + b)(a^2 - ab + b^2).

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